A solution of the Zeno paradoxes in terms of a discrete space is usually rejected on the basis of an argument formulated by Hermann Weyl, the so-called tile argument. This note shows that, given a set of reasonable assumptions for a discrete geometry, the Weyl argument does not apply. The crucial step is to stress the importance of the nonzero width of a line. The Pythagorean theorem is shown to hold for arbitrary right triangles.